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|
structure Tree: TREE = struct
datatype ('k, 'v) t = Node of 'k * 'v * ('k, 'v) t * ('k, 'v) t | Empty
type 'k cmp = 'k -> 'k -> order
val empty = Empty
fun insert _ Empty k v = (NONE, Node (k, v, Empty, Empty))
| insert cmp (Node (k', v', left, right)) k v =
case cmp k k' of
LESS =>
let
val (res, left) = insert cmp left k v
in
(res, Node (k', v', left, right))
end
| EQUAL => (SOME v', Node (k, v, left, right))
| GREATER =>
let
val (res, right) = insert cmp right k v
in
(res, Node (k', v', left, right))
end
fun delete _ Empty _ = (NONE, Empty)
| delete cmp (Node (k', v', left, right)) k =
case cmp k k' of
LESS =>
let
val (res, left) = delete cmp left k
in
(res, Node (k', v', left, right))
end
| GREATER =>
let
val (res, right) = delete cmp right k
in
(res, Node (k', v', left, right))
end
| EQUAL => (
case (left, right) of
(Empty, Node _) => (SOME v', right)
| (Node _, Empty) => (SOME v', left)
| (Empty, Empty) => (SOME v', Empty)
| (Node _, Node _) =>
let
fun deleteRightmost Empty = raise Unreachable
| deleteRightmost (Node (k, v, left, Empty)) =
((k, v), left)
| deleteRightmost (Node (k, v, left, right)) =
let
val (p, right) = deleteRightmost right
in
(p, Node (k, v, left, right))
end
val ((k, v), left) = deleteRightmost left
in
(SOME v', Node (k, v, left, right))
end
)
fun lookup _ Empty _ = NONE
| lookup cmp (Node (k', v', left, right)) k =
case cmp k k' of
LESS => lookup cmp left k
| EQUAL => SOME v'
| GREATER => lookup cmp right k
datatype ('k, 'v) arc =
Left of 'k * 'v * ('k, 'v) t |
Right of 'k * 'v * ('k, 'v) t
fun assemble buf n =
let
fun assemble' (Left (k, v, right) :: tail) tree =
assemble' tail (Node (k, v, tree, right))
| assemble' (Right (k, v, left) :: tail) tree =
assemble' tail (Node (k, v, left, tree))
| assemble' [] tree = tree
in
assemble' buf n
end
(* f accepts previous value (NONE if not present) and returns
* (res, v' option). Res will be returned by lookup2. 'v if present, will
* be new value in place of the old one
*)
fun lookup' buf _ Empty k f =
let
val (res, newV) = f NONE
in
(res, assemble buf
(case newV of
NONE => Empty
| SOME v => Node (k, v, Empty, Empty)))
end
| lookup' buf cmp (T as Node (k', v', left, right)) k f =
case cmp k k' of
LESS => lookup' (Left (k', v', right) :: buf) cmp left k f
| GREATER => lookup' (Right (k', v', left) :: buf) cmp right k f
| EQUAL =>
let
val (res, newV) = f $ SOME v'
in
case newV of
NONE => (res, T)
| SOME v => (res, assemble buf (Node (k', v, left, right)))
end
fun lookup2 cmp t k f = lookup' [] cmp t k f
fun print t key2str value2str =
let
fun Pkey z = bindWith2str key2str z
fun Pvalue z = bindWith2str value2str z
fun print' off Empty = printf R off `"()\n" %
| print' off (Node (k, v, left, right)) = (
printf R off `"(" Pkey k `", " Pvalue v `"\n";
print' (off + 1) left;
print' (off + 1) right;
printf R off `")\n" %
)
in
print' 0 t
end
fun size Empty = 0
| size (Node(_, _, l, r)) = 1 + size l + size r
end
|
